http://www.perlmonks.org?node_id=1197795

Another "Silly use for Perl" entry.

Anonymous Monk asked for a method for incrementing mixed letters and numbers recently, which particular need is satisfied with Math::Base36. Can we do better? I guess, yes.

```use 5.10.0;
use Math::Base;

my \$begin = Math::Base->new(36, 1009, 1); # base, number, is_encoded
my \$end   = Math::Base->new(36, 1020, 1);
my \$c     = Math::Base->new(36, 42);

say \$c->encode(\$_) for \$begin .. \$end;

# 1009
# 100A
# 100B
# 100C
# ...
# 101X
# 101Y
# 101Z
# 1020

# also (with updated code below)
# my \$x = Math::Base->new(36, 46664); # 1008 in base36
# say ++\$x for 0..63; # output same as above

# Arithmetics with different encodings:

\$p = Math::Base->new(8,777,1); # decimal 511
\$z = Math::Base->new(36, 35);  # 'Z' as base36
say \$z * \$p;                   # 42735 (octal)
say \$p * \$z;                   # 'DST' (base36)

# Changing the string representation:

\$s = Math::Base->new(16,18);
say \$s;                        # 12
\$s->rebase(18);
say \$s;                        # 10
\$s += 3;                       # 13
\$s->rebase(2);
say \$s;                        # 10101

# Get decimal value:

\$xyz = Math::Base->new(64, 'XYZabc', 1);
say \$xyz->num;                 # 36013230438

Far from complete, but fun enough yet. For me, that is... ;-)

Update: Below is an updated version which handles negative numbers, implements missing operators and lets you define your own charset for baseX conversion, e.g. to calculate base3 with qw(a b c). Also, a method integer() is added which emulates use integer globally for all calculations, and some utility methods/functions.

Update: fixed some bugs

I'll eventually make it into a CPAN package proper.

perl -le'print map{pack c,(\$-++?1:13)+ord}split//,ESEL'

Replies are listed 'Best First'.
Re: Math::Base - arithmetics with baseX integers
by no_slogan (Deacon) on Aug 22, 2017 at 14:32 UTC
This is a neat idea, but encode spins forever when \$num is negative and returns an empty string when it's zero. You could do this:
```    my \$val = abs(\$num);
do {
push @ret, \$chars[\$val % \$base];
\$val = int(\$val / \$base);
} while \$val;
push @ret, '-' if \$num < 0;
But '-' is in the @chars array.

What I did is to mimic the behavior of sprintf and hex in encode(), i.e. roll over:

```    \$num = (~abs(\$num))+1 if \$num < 0;

And the return line now reads:

```       return join( '', reverse @ret) || 0;

I've updated the op with the new version. Thanks for your hints!

perl -le'print map{pack c,(\$-++?1:13)+ord}split//,ESEL'
\$num = int \$num;
\$num = (~abs(\$num))+1 if \$num < 0;

You can get the same effect with \$num |= 0; ...but... why? Why would you want two's complement behavior in other bases?

Truncating at \$n bits is mathematically equivalent to:

\$num %= 2 ** \$n;

That's only meaningful for base-2. You can truncate at \$n base-\$b digits using this:

\$num %= \$b ** \$n;

So -1 becomes 999999 in base-10 or 666666 in base-7. If you want, you can pick a big number of digits that still fits in a double-precision float like this:

\$num %= \$base ** int(36.73/log(\$base));

This is one of the reasons why I wrote Far from complete (besides missing pod, tests, you name it.)

The perl builtins suffer from negative integer flaws also. The format %x of sprintf expects a signed an unsigned integer, but nonetheless

```say \$f = sprintf "%x", -15;
say hex \$f;
__END__
fffffffffffffff1
18446744073709551601

on a 64bit system. The object could get a sign flag set by the constructor which is honored by arithmetic operations, but the string representation would be ambiguous anyways if the string has a leading dash.

I'm not sure what to do about that. Perhaps limiting to unsigned integers is the way to go, and encode should croak if the number is negative; don't know yet.

update: unsigned, yes, that's the point; common typo. It is coerced into an unsigned. Thanks Anonymous Monk fo pointing out the glitch.

perl -le'print map{pack c,(\$-++?1:13)+ord}split//,ESEL'
%x is clearly documented as taking an unsigned int in the page you link to.
Re: Math::Base - arithmetics with baseX integers
by hdb (Monsignor) on Aug 22, 2017 at 12:54 UTC

Here is my favorite example:

```use Math::Base;

my \$one = Math::Base->new( 13, 6 );
my \$two = Math::Base->new( 13, 9 );

print "\$one times \$two equals ", \$one*\$two, " base 13.\n";